Textures are shifted in Cycles render
It looks like you have already unwrapped your model, so I am guessing that the problem is that Cycles isn't using the UV map you have created.

To tell Cycles explicitly to use a particular UV map add an Input > UV Map node and plug it into the Vector input on your image texture.  Make sure that the correct UV map is selected on the UV map node.





Alternatively, you can check which UV map is being used as the default UV map under Object Data properties panel > UV Maps rollout.  You can set the default UV map by clicking on the small camera icon next to it.



This will only have an effect if there are no mapping coordinates explicitly defined for a texture as above.